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Waveform relaxation as a dynamical system

Bjørhus, Morten and Stuart, Andrew M. (1997) Waveform relaxation as a dynamical system. Mathematics of Computation, 66 (219). pp. 1101-1118. ISSN 0025-5718. doi:10.1090/S0025-5718-97-00847-8.

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In this paper the properties of waveform relaxation are studied when applied to the dynamical system generated by an autonomous ordinary differential equation. In particular, the effect of the waveform relaxation on the invariant sets of the flow is analysed. Windowed waveform relaxation is studied, whereby the iterative technique is applied on successive time intervals of length T and a fixed, finite, number of iterations taken on each window. This process does not generate a dynamical system on R+ since two different applications of the waveform algorithm over different time intervals do not, in general, commute. In order to generate a dynamical system it is necessary to consider the time T map generated by the relaxation process. This is done, and C^1-closeness of the resulting map to the time T map of the underlying ordinary differential equation is established. Using this, various results from the theory of dynamical systems are applied, and the results discussed.

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Additional Information:© 1997 American Mathematical Society. Received by the editor December 19, 1994 and, in revised form, October 16, 1995. The first author was supported by the Research Council of Norway. The second author was supported by the National Science Foundation and the Office for Naval Research.
Funding AgencyGrant Number
Research Council of NorwayUNSPECIFIED
Office of Naval Research (ONR)UNSPECIFIED
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ35
Issue or Number:219
Classification Code:1991 Mathematics Subject Classification: Primary 65L05, 34C35, 65Q05
Record Number:CaltechAUTHORS:20170612-145717225
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78126
Deposited By: Tony Diaz
Deposited On:12 Jun 2017 22:05
Last Modified:15 Nov 2021 17:37

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